When I saw the /v1 prefix I was reminded of one of Steve Klabnik's blog posts[1], where he gives an alternative, arguably more RESTful approach to versioning an API.
[1]: http://blog.steveklabnik.com/posts/2011-07-03-nobody-underst...
[1]: http://blog.steveklabnik.com/posts/2011-07-03-nobody-underst...
It's like this:
--> GET /api/ Accept: application/json
<-- Content-type: application/vnd.api.v1+json <stuff>
Then your consumers can know what version of the API they're interacting with and act accordingly.
Including the version number in the URL gets around this and even allows you to test API responses in mobile browsers if needed.
Although I tend to agree that a header-based approach is cleaner and more in the spirit of REST and even HTTP.